Probation isn't just for one set of team kills, either, never mind one team kill.
To some of the above, it isn't your team mates jobs to dodge your bullets. Our clan is basically Hardcore only and we've had plenty of times we've saved each other with an enemy in knifing range with well placed bullets. I have been kicked a few times through scorestreaks, but a lot of that has been cleared up. Now I mostly get kicked because I've shot an idiot team mate who's just killed me for being too close to their precious tags.
When you use explosives on hardcore you take that chance. After many times of teammates throwing grenades and causing me to run away from them only to get killed by enemy, I now will let that grenade kill me. Then I leave no tag for enemy and take no death.
Do not like it? Then do not team kill. Play smarter and think before tossing yoru nade randomly someplace. Pay more attention to the location of teammates and where they are going before tossing a nade. Total number of times I have got probation from TK... 0... So clearly it is a problem on your end and how you play, and that you yourself need to adapt and change your tactics and playstyle instead.
I too have been getting kicked for 1 team kill
OP needs to start telling the truth, it wasn't one kill dude.